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   "source": [
    "# The Mathematical Engineering of Deep Learning\n",
    "\n",
    "## Practical 4 (Julia version)\n",
    "**For an R or Python version see the [course website](https://deeplearningmath.org/)**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nrow = 400\n"
     ]
    },
    {
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       "<table class=\"data-frame\"><thead><tr><th></th><th>x1</th><th>x2</th><th>y</th></tr><tr><th></th><th>Float64</th><th>Float64</th><th>Float64</th></tr></thead><tbody><p>6 rows × 3 columns</p><tr><th>1</th><td>1.20444</td><td>3.57611</td><td>0.0</td></tr><tr><th>2</th><td>0.15871</td><td>-1.48217</td><td>0.0</td></tr><tr><th>3</th><td>0.0952472</td><td>-1.27996</td><td>0.0</td></tr><tr><th>4</th><td>0.349178</td><td>-2.06438</td><td>0.0</td></tr><tr><th>5</th><td>0.69415</td><td>2.88911</td><td>0.0</td></tr><tr><th>6</th><td>1.62065</td><td>-4.03512</td><td>0.0</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& x1 & x2 & y\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1.20444 & 3.57611 & 0.0 \\\\\n",
       "\t2 & 0.15871 & -1.48217 & 0.0 \\\\\n",
       "\t3 & 0.0952472 & -1.27996 & 0.0 \\\\\n",
       "\t4 & 0.349178 & -2.06438 & 0.0 \\\\\n",
       "\t5 & 0.69415 & 2.88911 & 0.0 \\\\\n",
       "\t6 & 1.62065 & -4.03512 & 0.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "6×3 DataFrame\n",
       "│ Row │ x1        │ x2       │ y       │\n",
       "│     │ \u001b[90mFloat64\u001b[39m   │ \u001b[90mFloat64\u001b[39m  │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼───────────┼──────────┼─────────┤\n",
       "│ 1   │ 1.20444   │ 3.57611  │ 0.0     │\n",
       "│ 2   │ 0.15871   │ -1.48217 │ 0.0     │\n",
       "│ 3   │ 0.0952472 │ -1.27996 │ 0.0     │\n",
       "│ 4   │ 0.349178  │ -2.06438 │ 0.0     │\n",
       "│ 5   │ 0.69415   │ 2.88911  │ 0.0     │\n",
       "│ 6   │ 1.62065   │ -4.03512 │ 0.0     │"
      ]
     },
     "execution_count": 353,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using RData, DataFrames, Random\n",
    "Random.seed!(10)\n",
    "df = load(\"planar_solar.RData\")[\"planarsolar\"]\n",
    "nrow = size(df)[1]\n",
    "@show nrow\n",
    "# df = df[shuffle(1:nrow),:]\n",
    "head(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 354,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 354,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using StatsPlots, LaTeXStrings\n",
    "@df df scatter(:x1,:x2,group = :y,xlabel=L\"x_1\",ylabel=L\"x_2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "size(train) = (320, 3)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>x1</th><th>x2</th><th>y</th></tr><tr><th></th><th>Float64</th><th>Float64</th><th>Float64</th></tr></thead><tbody><p>6 rows × 3 columns</p><tr><th>1</th><td>1.20444</td><td>3.57611</td><td>0.0</td></tr><tr><th>2</th><td>0.15871</td><td>-1.48217</td><td>0.0</td></tr><tr><th>3</th><td>0.0952472</td><td>-1.27996</td><td>0.0</td></tr><tr><th>4</th><td>0.349178</td><td>-2.06438</td><td>0.0</td></tr><tr><th>5</th><td>0.69415</td><td>2.88911</td><td>0.0</td></tr><tr><th>6</th><td>1.62065</td><td>-4.03512</td><td>0.0</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& x1 & x2 & y\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1.20444 & 3.57611 & 0.0 \\\\\n",
       "\t2 & 0.15871 & -1.48217 & 0.0 \\\\\n",
       "\t3 & 0.0952472 & -1.27996 & 0.0 \\\\\n",
       "\t4 & 0.349178 & -2.06438 & 0.0 \\\\\n",
       "\t5 & 0.69415 & 2.88911 & 0.0 \\\\\n",
       "\t6 & 1.62065 & -4.03512 & 0.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "6×3 DataFrame\n",
       "│ Row │ x1        │ x2       │ y       │\n",
       "│     │ \u001b[90mFloat64\u001b[39m   │ \u001b[90mFloat64\u001b[39m  │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼───────────┼──────────┼─────────┤\n",
       "│ 1   │ 1.20444   │ 3.57611  │ 0.0     │\n",
       "│ 2   │ 0.15871   │ -1.48217 │ 0.0     │\n",
       "│ 3   │ 0.0952472 │ -1.27996 │ 0.0     │\n",
       "│ 4   │ 0.349178  │ -2.06438 │ 0.0     │\n",
       "│ 5   │ 0.69415   │ 2.88911  │ 0.0     │\n",
       "│ 6   │ 1.62065   │ -4.03512 │ 0.0     │"
      ]
     },
     "execution_count": 355,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_test_split_index = Int(nrow*0.8)\n",
    "train = df[1:train_test_split_index,:]\n",
    "@show size(train)\n",
    "head(train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "size(test) = (80, 3)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>x1</th><th>x2</th><th>y</th></tr><tr><th></th><th>Float64</th><th>Float64</th><th>Float64</th></tr></thead><tbody><p>6 rows × 3 columns</p><tr><th>1</th><td>-2.12767</td><td>1.38667</td><td>1.0</td></tr><tr><th>2</th><td>-2.96425</td><td>0.590891</td><td>1.0</td></tr><tr><th>3</th><td>-3.60274</td><td>1.299</td><td>1.0</td></tr><tr><th>4</th><td>-1.17473</td><td>0.965871</td><td>1.0</td></tr><tr><th>5</th><td>-2.58752</td><td>1.56882</td><td>1.0</td></tr><tr><th>6</th><td>-3.16294</td><td>1.7693</td><td>1.0</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& x1 & x2 & y\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & -2.12767 & 1.38667 & 1.0 \\\\\n",
       "\t2 & -2.96425 & 0.590891 & 1.0 \\\\\n",
       "\t3 & -3.60274 & 1.299 & 1.0 \\\\\n",
       "\t4 & -1.17473 & 0.965871 & 1.0 \\\\\n",
       "\t5 & -2.58752 & 1.56882 & 1.0 \\\\\n",
       "\t6 & -3.16294 & 1.7693 & 1.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "6×3 DataFrame\n",
       "│ Row │ x1       │ x2       │ y       │\n",
       "│     │ \u001b[90mFloat64\u001b[39m  │ \u001b[90mFloat64\u001b[39m  │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼──────────┼──────────┼─────────┤\n",
       "│ 1   │ -2.12767 │ 1.38667  │ 1.0     │\n",
       "│ 2   │ -2.96425 │ 0.590891 │ 1.0     │\n",
       "│ 3   │ -3.60274 │ 1.299    │ 1.0     │\n",
       "│ 4   │ -1.17473 │ 0.965871 │ 1.0     │\n",
       "│ 5   │ -2.58752 │ 1.56882  │ 1.0     │\n",
       "│ 6   │ -3.16294 │ 1.7693   │ 1.0     │"
      ]
     },
     "execution_count": 356,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test = df[(train_test_split_index+1):nrow,:]\n",
    "@show size(test)\n",
    "head(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = convert(Matrix,train[:,[:x1,:x2]])'\n",
    "y_train = train.y\n",
    "\n",
    "x_test = convert(Matrix,test[:,[:x1,:x2]])'\n",
    "y_test = test.y;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 358,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "σ (generic function with 1 method)"
      ]
     },
     "execution_count": 358,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ(x) = 1/(1+exp(-x))  #Use \\sigma + [TAB] for σ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "getLayerSize (generic function with 1 method)"
      ]
     },
     "execution_count": 359,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function getLayerSize(X,y)\n",
    "    ls = Dict()\n",
    "    ls[:n_x] = size(X)[1]\n",
    "    ls[:m] = size(X)[2]\n",
    "    ls[:n_y] = 1\n",
    "    return ls\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "initializeParameters (generic function with 1 method)"
      ]
     },
     "execution_count": 360,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Distributions\n",
    "\n",
    "function initializeParameters(dict_layer_size)\n",
    "    W1 = rand(Normal(0,1),dict_layer_size[:n_y],dict_layer_size[:n_x])\n",
    "    b1 = fill(0.0,dict_layer_size[:n_y],1)\n",
    "    params = Dict()\n",
    "    params[:W1] = W1\n",
    "    params[:b1] = b1\n",
    "    return params\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "forwardPropagation (generic function with 1 method)"
      ]
     },
     "execution_count": 361,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function forwardPropagation(X,params,list_layer_size)\n",
    "    Z1 = params[:W1]*X .+ params[:b1]\n",
    "    A1 = σ.(Z1)\n",
    "    cache = Dict()\n",
    "    cache[:Z1] = Z1\n",
    "    cache[:A1] = A1\n",
    "    return cache\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "computeCost (generic function with 1 method)"
      ]
     },
     "execution_count": 362,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Statistics\n",
    "ϵ = 1e-8\n",
    "computeCost(y,cache) = -mean(log.(cache[:A1].+ ϵ) .* y  + log.(1 .- cache[:A1] .+ ϵ).*(1 .- y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "backwardPropagation (generic function with 1 method)"
      ]
     },
     "execution_count": 363,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function backwardPropagation(X,y,cache,params,list_layer_size)\n",
    "    dZ1 = cache[:A1] - y'\n",
    "    dW1 = (1/list_layer_size[:m])*dZ1*X'\n",
    "    db1 = (1/list_layer_size[:m])*sum(dZ1)\n",
    "    grads = Dict()\n",
    "    grads[:dW1] = dW1\n",
    "    grads[:db1] = db1\n",
    "    return grads\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "updateParameters (generic function with 1 method)"
      ]
     },
     "execution_count": 364,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function updateParameters(grads,params,η) # \\eta + [TAB]\n",
    "    W1 = params[:W1] .- η*grads[:dW1]\n",
    "    b1 = params[:b1] .- η*grads[:db1]\n",
    "    newParams = Dict()\n",
    "    newParams[:W1] = W1\n",
    "    newParams[:b1] = b1\n",
    "    return newParams\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {},
   "outputs": [],
   "source": [
    "##### This is here to debug\n",
    "# ls = getLayerSize(x_train,y_train)\n",
    "# pr = initializeParameters(ls)\n",
    "# ch = forwardPropagation(x_train,pr,ls)\n",
    "# cst = computeCost(y_train,ch)\n",
    "# @show cst\n",
    "# gr = backwardPropagation(x_train,y_train,ch,pr,ls)\n",
    "# updateParameters(gr,pr,0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "trainModel (generic function with 1 method)"
      ]
     },
     "execution_count": 365,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function trainModel(X,y,num_iterations,η)\n",
    "    ls = getLayerSize(X,y)\n",
    "    pr = initializeParameters(ls)\n",
    "    costHistory = []\n",
    "    \n",
    "    for i in 1:num_iterations\n",
    "        ch = forwardPropagation(X,pr,ls)\n",
    "        cost = computeCost(y,ch)\n",
    "        push!(costHistory,cost)\n",
    "        gr = backwardPropagation(X,y,ch,pr,ls)\n",
    "        pr = updateParameters(gr,pr,η)\n",
    "        i % 10 == 0 && print(\".\")\n",
    "    end\n",
    "    \n",
    "    modelOut = Dict()\n",
    "    modelOut[:params] = pr\n",
    "    modelOut[:costHist] = costHistory\n",
    "    return modelOut\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "...................................................................................................."
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{Any,Any} with 2 entries:\n",
       "  :params   => Dict{Any,Any}(:W1=>[0.14036 -0.203539],:b1=>[-0.443863])\n",
       "  :costHist => Any[0.879176, 0.876257, 0.873364, 0.870497, 0.867657, 0.864843, …"
      ]
     },
     "execution_count": 369,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1 = trainModel(x_train,y_train,1000,0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "metadata": {},
   "outputs": [
    {
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       "  577.47,1312.39 579.467,1314.43 581.464,1316.42 583.461,1318.38 585.458,1320.28 587.455,1322.15 589.452,1323.97 591.449,1325.75 593.446,1327.5 595.443,1329.2 \n",
       "  597.44,1330.86 599.437,1332.48 601.434,1334.07 603.431,1335.62 605.428,1337.13 607.425,1338.6 609.422,1340.04 611.419,1341.45 613.416,1342.82 615.413,1344.16 \n",
       "  617.41,1345.47 619.407,1346.74 621.404,1347.99 623.401,1349.2 625.398,1350.38 627.395,1351.53 629.392,1352.66 631.389,1353.75 633.386,1354.82 635.383,1355.86 \n",
       "  637.38,1356.87 639.377,1357.85 641.374,1358.81 643.371,1359.75 645.368,1360.66 647.366,1361.54 649.363,1362.4 651.36,1363.24 653.357,1364.06 655.354,1364.85 \n",
       "  657.351,1365.62 659.348,1366.36 661.345,1367.09 663.342,1367.8 665.339,1368.48 667.336,1369.15 669.333,1369.79 671.33,1370.42 673.327,1371.03 675.324,1371.62 \n",
       "  677.321,1372.19 679.318,1372.74 681.315,1373.28 683.312,1373.79 685.309,1374.3 687.306,1374.78 689.303,1375.25 691.3,1375.71 693.297,1376.14 695.294,1376.57 \n",
       "  697.291,1376.98 699.288,1377.37 701.285,1377.75 703.282,1378.12 705.279,1378.47 707.276,1378.81 709.273,1379.14 711.27,1379.45 713.267,1379.75 715.264,1380.04 \n",
       "  717.261,1380.32 719.258,1380.58 721.255,1380.84 723.252,1381.08 725.249,1381.31 727.246,1381.54 729.243,1381.75 731.24,1381.95 733.237,1382.14 735.234,1382.32 \n",
       "  737.231,1382.49 739.228,1382.65 741.225,1382.81 743.222,1382.95 745.219,1383.09 747.216,1383.21 749.213,1383.33 751.21,1383.44 753.207,1383.55 755.204,1383.64 \n",
       "  757.201,1383.73 759.198,1383.81 761.195,1383.88 763.192,1383.94 765.189,1384 767.186,1384.05 769.183,1384.1 771.18,1384.14 773.177,1384.17 775.174,1384.19 \n",
       "  777.171,1384.21 779.168,1384.23 781.165,1384.24 783.162,1384.24 785.16,1384.24 787.157,1384.23 789.154,1384.21 791.151,1384.2 793.148,1384.17 795.145,1384.14 \n",
       "  797.142,1384.11 799.139,1384.07 801.136,1384.03 803.133,1383.98 805.13,1383.93 807.127,1383.88 809.124,1383.82 811.121,1383.76 813.118,1383.69 815.115,1383.62 \n",
       "  817.112,1383.55 819.109,1383.47 821.106,1383.39 823.103,1383.3 825.1,1383.22 827.097,1383.12 829.094,1383.03 831.091,1382.93 833.088,1382.83 835.085,1382.73 \n",
       "  837.082,1382.63 839.079,1382.52 841.076,1382.41 843.073,1382.3 845.07,1382.18 847.067,1382.06 849.064,1381.94 851.061,1381.82 853.058,1381.7 855.055,1381.57 \n",
       "  857.052,1381.44 859.049,1381.31 861.046,1381.18 863.043,1381.04 865.04,1380.91 867.037,1380.77 869.034,1380.63 871.031,1380.49 873.028,1380.35 875.025,1380.2 \n",
       "  877.022,1380.06 879.019,1379.91 881.016,1379.76 883.013,1379.61 885.01,1379.46 887.007,1379.31 889.004,1379.16 891.001,1379 892.998,1378.85 894.995,1378.69 \n",
       "  896.992,1378.53 898.989,1378.37 900.986,1378.22 902.983,1378.06 904.98,1377.9 906.977,1377.73 908.974,1377.57 910.971,1377.41 912.968,1377.25 914.965,1377.08 \n",
       "  916.962,1376.92 918.959,1376.75 920.956,1376.59 922.953,1376.42 924.951,1376.25 926.948,1376.09 928.945,1375.92 930.942,1375.75 932.939,1375.58 934.936,1375.41 \n",
       "  936.933,1375.25 938.93,1375.08 940.927,1374.91 942.924,1374.74 944.921,1374.57 946.918,1374.4 948.915,1374.23 950.912,1374.06 952.909,1373.89 954.906,1373.72 \n",
       "  956.903,1373.55 958.9,1373.38 960.897,1373.21 962.894,1373.04 964.891,1372.87 966.888,1372.7 968.885,1372.53 970.882,1372.36 972.879,1372.19 974.876,1372.02 \n",
       "  976.873,1371.85 978.87,1371.68 980.867,1371.51 982.864,1371.34 984.861,1371.17 986.858,1371 988.855,1370.84 990.852,1370.67 992.849,1370.5 994.846,1370.33 \n",
       "  996.843,1370.17 998.84,1370 1000.84,1369.83 1002.83,1369.67 1004.83,1369.5 1006.83,1369.34 1008.83,1369.17 1010.82,1369.01 1012.82,1368.84 1014.82,1368.68 \n",
       "  1016.81,1368.52 1018.81,1368.35 1020.81,1368.19 1022.8,1368.03 1024.8,1367.87 1026.8,1367.71 1028.8,1367.55 1030.79,1367.39 1032.79,1367.23 1034.79,1367.07 \n",
       "  1036.78,1366.91 1038.78,1366.75 1040.78,1366.59 1042.77,1366.44 1044.77,1366.28 1046.77,1366.12 1048.77,1365.97 1050.76,1365.81 1052.76,1365.66 1054.76,1365.5 \n",
       "  1056.75,1365.35 1058.75,1365.2 1060.75,1365.05 1062.74,1364.9 1064.74,1364.74 1066.74,1364.59 1068.74,1364.44 1070.73,1364.3 1072.73,1364.15 1074.73,1364 \n",
       "  1076.72,1363.85 1078.72,1363.71 1080.72,1363.56 1082.71,1363.41 1084.71,1363.27 1086.71,1363.12 1088.71,1362.98 1090.7,1362.84 1092.7,1362.7 1094.7,1362.55 \n",
       "  1096.69,1362.41 1098.69,1362.27 1100.69,1362.13 1102.68,1361.99 1104.68,1361.86 1106.68,1361.72 1108.68,1361.58 1110.67,1361.44 1112.67,1361.31 1114.67,1361.17 \n",
       "  1116.66,1361.04 1118.66,1360.91 1120.66,1360.77 1122.65,1360.64 1124.65,1360.51 1126.65,1360.38 1128.65,1360.25 1130.64,1360.12 1132.64,1359.99 1134.64,1359.86 \n",
       "  1136.63,1359.73 1138.63,1359.6 1140.63,1359.48 1142.63,1359.35 1144.62,1359.23 1146.62,1359.1 1148.62,1358.98 1150.61,1358.85 1152.61,1358.73 1154.61,1358.61 \n",
       "  1156.6,1358.49 1158.6,1358.37 1160.6,1358.25 1162.6,1358.13 1164.59,1358.01 1166.59,1357.89 1168.59,1357.77 1170.58,1357.66 1172.58,1357.54 1174.58,1357.42 \n",
       "  1176.57,1357.31 1178.57,1357.2 1180.57,1357.08 1182.57,1356.97 1184.56,1356.86 1186.56,1356.75 1188.56,1356.63 1190.55,1356.52 1192.55,1356.41 1194.55,1356.31 \n",
       "  1196.54,1356.2 1198.54,1356.09 1200.54,1355.98 1202.54,1355.88 1204.53,1355.77 1206.53,1355.66 1208.53,1355.56 1210.52,1355.46 1212.52,1355.35 1214.52,1355.25 \n",
       "  1216.51,1355.15 1218.51,1355.05 1220.51,1354.95 1222.51,1354.85 1224.5,1354.75 1226.5,1354.65 1228.5,1354.55 1230.49,1354.45 1232.49,1354.35 1234.49,1354.26 \n",
       "  1236.48,1354.16 1238.48,1354.07 1240.48,1353.97 1242.48,1353.88 1244.47,1353.78 1246.47,1353.69 1248.47,1353.6 1250.46,1353.51 1252.46,1353.41 1254.46,1353.32 \n",
       "  1256.45,1353.23 1258.45,1353.14 1260.45,1353.05 1262.45,1352.97 1264.44,1352.88 1266.44,1352.79 1268.44,1352.7 1270.43,1352.62 1272.43,1352.53 1274.43,1352.45 \n",
       "  1276.43,1352.36 1278.42,1352.28 1280.42,1352.2 1282.42,1352.11 1284.41,1352.03 1286.41,1351.95 1288.41,1351.87 1290.4,1351.79 1292.4,1351.71 1294.4,1351.63 \n",
       "  1296.4,1351.55 1298.39,1351.47 1300.39,1351.39 1302.39,1351.31 1304.38,1351.24 1306.38,1351.16 1308.38,1351.08 1310.37,1351.01 1312.37,1350.93 1314.37,1350.86 \n",
       "  1316.37,1350.79 1318.36,1350.71 1320.36,1350.64 1322.36,1350.57 1324.35,1350.49 1326.35,1350.42 1328.35,1350.35 1330.34,1350.28 1332.34,1350.21 1334.34,1350.14 \n",
       "  1336.34,1350.07 1338.33,1350 1340.33,1349.94 1342.33,1349.87 1344.32,1349.8 1346.32,1349.74 1348.32,1349.67 1350.31,1349.6 1352.31,1349.54 1354.31,1349.47 \n",
       "  1356.31,1349.41 1358.3,1349.35 1360.3,1349.28 1362.3,1349.22 1364.29,1349.16 1366.29,1349.09 1368.29,1349.03 1370.28,1348.97 1372.28,1348.91 1374.28,1348.85 \n",
       "  1376.28,1348.79 1378.27,1348.73 1380.27,1348.67 1382.27,1348.61 1384.26,1348.56 1386.26,1348.5 1388.26,1348.44 1390.25,1348.38 1392.25,1348.33 1394.25,1348.27 \n",
       "  1396.25,1348.22 1398.24,1348.16 1400.24,1348.1 1402.24,1348.05 1404.23,1348 1406.23,1347.94 1408.23,1347.89 1410.23,1347.84 1412.22,1347.78 1414.22,1347.73 \n",
       "  1416.22,1347.68 1418.21,1347.63 1420.21,1347.58 1422.21,1347.53 1424.2,1347.48 1426.2,1347.43 1428.2,1347.38 1430.2,1347.33 1432.19,1347.28 1434.19,1347.23 \n",
       "  1436.19,1347.18 1438.18,1347.14 1440.18,1347.09 1442.18,1347.04 1444.17,1346.99 1446.17,1346.95 1448.17,1346.9 1450.17,1346.86 1452.16,1346.81 1454.16,1346.77 \n",
       "  1456.16,1346.72 1458.15,1346.68 1460.15,1346.63 1462.15,1346.59 1464.14,1346.55 1466.14,1346.51 1468.14,1346.46 1470.14,1346.42 1472.13,1346.38 1474.13,1346.34 \n",
       "  1476.13,1346.3 1478.12,1346.26 1480.12,1346.21 1482.12,1346.17 1484.11,1346.13 1486.11,1346.09 1488.11,1346.06 1490.11,1346.02 1492.1,1345.98 1494.1,1345.94 \n",
       "  1496.1,1345.9 1498.09,1345.86 1500.09,1345.83 1502.09,1345.79 1504.08,1345.75 1506.08,1345.72 1508.08,1345.68 1510.08,1345.64 1512.07,1345.61 1514.07,1345.57 \n",
       "  1516.07,1345.54 1518.06,1345.5 1520.06,1345.47 1522.06,1345.43 1524.05,1345.4 1526.05,1345.36 1528.05,1345.33 1530.05,1345.3 1532.04,1345.27 1534.04,1345.23 \n",
       "  1536.04,1345.2 1538.03,1345.17 1540.03,1345.14 1542.03,1345.1 1544.02,1345.07 1546.02,1345.04 1548.02,1345.01 1550.02,1344.98 1552.01,1344.95 1554.01,1344.92 \n",
       "  1556.01,1344.89 1558,1344.86 1560,1344.83 1562,1344.8 1564,1344.77 1565.99,1344.74 1567.99,1344.72 1569.99,1344.69 1571.98,1344.66 1573.98,1344.63 \n",
       "  1575.98,1344.6 1577.97,1344.58 1579.97,1344.55 1581.97,1344.52 1583.97,1344.5 1585.96,1344.47 1587.96,1344.44 1589.96,1344.42 1591.95,1344.39 1593.95,1344.37 \n",
       "  1595.95,1344.34 1597.94,1344.32 1599.94,1344.29 1601.94,1344.27 1603.94,1344.24 1605.93,1344.22 1607.93,1344.19 1609.93,1344.17 1611.92,1344.15 1613.92,1344.12 \n",
       "  1615.92,1344.1 1617.91,1344.08 1619.91,1344.05 1621.91,1344.03 1623.91,1344.01 1625.9,1343.99 1627.9,1343.96 1629.9,1343.94 1631.89,1343.92 1633.89,1343.9 \n",
       "  1635.89,1343.88 1637.88,1343.86 1639.88,1343.84 1641.88,1343.81 1643.88,1343.79 1645.87,1343.77 1647.87,1343.75 1649.87,1343.73 1651.86,1343.71 1653.86,1343.69 \n",
       "  1655.86,1343.67 1657.85,1343.66 1659.85,1343.64 1661.85,1343.62 1663.85,1343.6 1665.84,1343.58 1667.84,1343.56 1669.84,1343.54 1671.83,1343.52 1673.83,1343.51 \n",
       "  1675.83,1343.49 1677.82,1343.47 1679.82,1343.45 1681.82,1343.44 1683.82,1343.42 1685.81,1343.4 1687.81,1343.39 1689.81,1343.37 1691.8,1343.35 1693.8,1343.34 \n",
       "  1695.8,1343.32 1697.8,1343.3 1699.79,1343.29 1701.79,1343.27 1703.79,1343.26 1705.78,1343.24 1707.78,1343.22 1709.78,1343.21 1711.77,1343.19 1713.77,1343.18 \n",
       "  1715.77,1343.16 1717.77,1343.15 1719.76,1343.14 1721.76,1343.12 1723.76,1343.11 1725.75,1343.09 1727.75,1343.08 1729.75,1343.06 1731.74,1343.05 1733.74,1343.04 \n",
       "  1735.74,1343.02 1737.74,1343.01 1739.73,1343 1741.73,1342.98 1743.73,1342.97 1745.72,1342.96 1747.72,1342.95 1749.72,1342.93 1751.71,1342.92 1753.71,1342.91 \n",
       "  1755.71,1342.9 1757.71,1342.88 1759.7,1342.87 1761.7,1342.86 1763.7,1342.85 1765.69,1342.84 1767.69,1342.82 1769.69,1342.81 1771.68,1342.8 1773.68,1342.79 \n",
       "  1775.68,1342.78 1777.68,1342.77 1779.67,1342.76 1781.67,1342.75 1783.67,1342.74 1785.66,1342.73 1787.66,1342.72 1789.66,1342.71 1791.65,1342.7 1793.65,1342.69 \n",
       "  1795.65,1342.68 1797.65,1342.67 1799.64,1342.66 1801.64,1342.65 1803.64,1342.64 1805.63,1342.63 1807.63,1342.62 1809.63,1342.61 1811.62,1342.6 1813.62,1342.59 \n",
       "  1815.62,1342.58 1817.62,1342.57 1819.61,1342.56 1821.61,1342.55 1823.61,1342.55 1825.6,1342.54 1827.6,1342.53 1829.6,1342.52 1831.6,1342.51 1833.59,1342.5 \n",
       "  1835.59,1342.5 1837.59,1342.49 1839.58,1342.48 1841.58,1342.47 1843.58,1342.46 1845.57,1342.46 1847.57,1342.45 1849.57,1342.44 1851.57,1342.43 1853.56,1342.43 \n",
       "  1855.56,1342.42 1857.56,1342.41 1859.55,1342.4 1861.55,1342.4 1863.55,1342.39 1865.54,1342.38 1867.54,1342.38 1869.54,1342.37 1871.54,1342.36 1873.53,1342.36 \n",
       "  1875.53,1342.35 1877.53,1342.34 1879.52,1342.34 1881.52,1342.33 1883.52,1342.32 1885.51,1342.32 1887.51,1342.31 1889.51,1342.31 1891.51,1342.3 1893.5,1342.29 \n",
       "  1895.5,1342.29 1897.5,1342.28 1899.49,1342.28 1901.49,1342.27 1903.49,1342.27 1905.48,1342.26 1907.48,1342.26 1909.48,1342.25 1911.48,1342.25 1913.47,1342.24 \n",
       "  1915.47,1342.23 1917.47,1342.23 1919.46,1342.22 1921.46,1342.22 1923.46,1342.21 1925.45,1342.21 1927.45,1342.21 1929.45,1342.2 1931.45,1342.2 1933.44,1342.19 \n",
       "  1935.44,1342.19 1937.44,1342.18 1939.43,1342.18 1941.43,1342.17 1943.43,1342.17 1945.42,1342.16 1947.42,1342.16 1949.42,1342.16 1951.42,1342.15 1953.41,1342.15 \n",
       "  1955.41,1342.14 1957.41,1342.14 1959.4,1342.14 1961.4,1342.13 1963.4,1342.13 1965.4,1342.13 1967.39,1342.12 1969.39,1342.12 1971.39,1342.11 1973.38,1342.11 \n",
       "  1975.38,1342.11 1977.38,1342.1 1979.37,1342.1 1981.37,1342.1 1983.37,1342.09 1985.37,1342.09 1987.36,1342.09 1989.36,1342.08 1991.36,1342.08 1993.35,1342.08 \n",
       "  1995.35,1342.08 1997.35,1342.07 1999.34,1342.07 2001.34,1342.07 2003.34,1342.06 2005.34,1342.06 2007.33,1342.06 2009.33,1342.06 2011.33,1342.05 2013.32,1342.05 \n",
       "  2015.32,1342.05 2017.32,1342.05 2019.31,1342.04 2021.31,1342.04 2023.31,1342.04 2025.31,1342.04 2027.3,1342.03 2029.3,1342.03 2031.3,1342.03 2033.29,1342.03 \n",
       "  2035.29,1342.02 2037.29,1342.02 2039.28,1342.02 2041.28,1342.02 2043.28,1342.02 2045.28,1342.01 2047.27,1342.01 2049.27,1342.01 2051.27,1342.01 2053.26,1342.01 \n",
       "  2055.26,1342 2057.26,1342 2059.25,1342 2061.25,1342 2063.25,1342 2065.25,1342 2067.24,1341.99 2069.24,1341.99 2071.24,1341.99 2073.23,1341.99 \n",
       "  2075.23,1341.99 2077.23,1341.99 2079.22,1341.99 2081.22,1341.98 2083.22,1341.98 2085.22,1341.98 2087.21,1341.98 2089.21,1341.98 2091.21,1341.98 2093.2,1341.98 \n",
       "  2095.2,1341.97 2097.2,1341.97 2099.19,1341.97 2101.19,1341.97 2103.19,1341.97 2105.19,1341.97 2107.18,1341.97 2109.18,1341.97 2111.18,1341.97 2113.17,1341.97 \n",
       "  2115.17,1341.96 2117.17,1341.96 2119.17,1341.96 2121.16,1341.96 2123.16,1341.96 2125.16,1341.96 2127.15,1341.96 2129.15,1341.96 2131.15,1341.96 2133.14,1341.96 \n",
       "  2135.14,1341.96 2137.14,1341.96 2139.14,1341.95 2141.13,1341.95 2143.13,1341.95 2145.13,1341.95 2147.12,1341.95 2149.12,1341.95 2151.12,1341.95 2153.11,1341.95 \n",
       "  2155.11,1341.95 2157.11,1341.95 2159.11,1341.95 2161.1,1341.95 2163.1,1341.95 2165.1,1341.95 2167.09,1341.95 2169.09,1341.95 2171.09,1341.95 2173.08,1341.95 \n",
       "  2175.08,1341.95 2177.08,1341.95 2179.08,1341.95 2181.07,1341.95 2183.07,1341.95 2185.07,1341.95 2187.06,1341.95 2189.06,1341.95 2191.06,1341.95 2193.05,1341.95 \n",
       "  2195.05,1341.95 2197.05,1341.95 2199.05,1341.94 2201.04,1341.94 2203.04,1341.94 2205.04,1341.94 2207.03,1341.94 2209.03,1341.94 2211.03,1341.94 2213.02,1341.94 \n",
       "  2215.02,1341.94 2217.02,1341.95 2219.02,1341.95 2221.01,1341.95 2223.01,1341.95 2225.01,1341.95 2227,1341.95 2229,1341.95 2231,1341.95 2232.99,1341.95 \n",
       "  2234.99,1341.95 2236.99,1341.95 2238.99,1341.95 2240.98,1341.95 2242.98,1341.95 2244.98,1341.95 2246.97,1341.95 2248.97,1341.95 2250.97,1341.95 2252.97,1341.95 \n",
       "  2254.96,1341.95 2256.96,1341.95 2258.96,1341.95 2260.95,1341.95 2262.95,1341.95 2264.95,1341.95 2266.94,1341.95 2268.94,1341.95 2270.94,1341.95 2272.94,1341.95 \n",
       "  2274.93,1341.95 2276.93,1341.95 2278.93,1341.95 2280.92,1341.95 2282.92,1341.95 2284.92,1341.96 2286.91,1341.96 2288.91,1341.96 2290.91,1341.96 2292.91,1341.96 \n",
       "  \n",
       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 370,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "plot(model1[:costHist],xlabel=\"Epoch\",ylabel=\"Cost\",legend=false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{GeneralizedLinearModel{GLM.GlmResp{Array{Float64,1},Binomial{Float64},LogitLink},GLM.DensePredChol{Float64,LinearAlgebra.Cholesky{Float64,Array{Float64,2}}}},Array{Float64,2}}\n",
       "\n",
       "y ~ 1 + x1 + x2\n",
       "\n",
       "Coefficients:\n",
       "──────────────────────────────────────────────────────────────────────────\n",
       "                 Coef.  Std. Error      z  Pr(>|z|)  Lower 95%   Upper 95%\n",
       "──────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)  -0.491795   0.118085   -4.16    <1e-4   -0.723237  -0.260353\n",
       "x1            0.142829   0.0617312   2.31    0.0207   0.021838   0.26382\n",
       "x2           -0.203348   0.0657304  -3.09    0.0020  -0.332177  -0.0745189\n",
       "──────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 371,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using GLM\n",
    "model2 = glm(@formula(y ~ x1 + x2), train, Binomial(), LogitLink())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 372,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 1: ([-0.4438626593381834], [0.14035969021310446 -0.2035387142119553])\n",
      "Model 2: [-0.491794750479451, 0.1428289860026892, -0.2033481835966192]\n"
     ]
    }
   ],
   "source": [
    "println(\"Model 1: \",(model1[:params][:b1],model1[:params][:W1]))\n",
    "println(\"Model 2: \", coef(model2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 373,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls = getLayerSize(x_train,y_train)\n",
    "\n",
    "gridX1 = (minimum(df.x1)-1):0.25:(maximum(df.x1)+1)\n",
    "gridX2 = (minimum(df.x2)-1):0.25:(maximum(df.x2)+1)\n",
    "grid = [[x1,x2]  for x1 in gridX1, x2 in gridX2]\n",
    "rule = [forwardPropagation(x,model1[:params],ls)[:A1][1] .> 0.5 for x in grid]\n",
    "heatmap(rule,flip=true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 374,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter(first.(vec(grid)),last.(vec(grid)),group = vec(rule))#,ms=3,c=[:red :black])\n",
    "@df df scatter!(:x1,:x2,group = :y,xlabel=L\"x_1\",ylabel=L\"x_2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding one hidden layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "feedforward (generic function with 1 method)"
      ]
     },
     "execution_count": 352,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function feedforward(x,w1,w2)\n",
    "    z1 = [1 x] * w1\n",
    "    a1 = σ.(z1)\n",
    "    z2 = [1 a1] * w2\n",
    "    Dict(:output => σ.(z2), :a1 => a1)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{Int64,Int64} with 2 entries:\n",
       "  3 => 4\n",
       "  1 => 2"
      ]
     },
     "execution_count": 350,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backpropagate <- function(x, y, y_hat, w1, w2, h, learn_rate) {\n",
    "#   dw2 <- t(cbind(1, h)) %*% (y_hat - y)\n",
    "#   dh  <- (y_hat - y) %*% t(w2[-1, , drop = FALSE])\n",
    "#   dw1 <- t(cbind(1, x)) %*% (h * (1 - h) * dh)\n",
    "  \n",
    "#   w1 <- w1 - learn_rate * dw1\n",
    "#   w2 <- w2 - learn_rate * dw2\n",
    "  \n",
    "#   list(w1 = w1, w2 = w2)\n",
    "# }\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function backpropagate(x,y,y_hat,w1,w2,a1,η)\n",
    "    dw2 = [1 a1]' * (yhat-y)\n",
    "    dh = (y_hat-y) * ()????\n",
    "    dw = [1 x]' * (a1*(1-a1)*da1)\n",
    "    \n",
    "    w1 = w1 - η*dw1\n",
    "    w2 = w2 - η*dw2\n",
    "    Dict(:w1 = w1, :w2 = w2)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function train(x,y; hidden = 5, η = 1e-2, iterations = 10^4 )\n",
    "\n",
    "end\n",
    "    \n",
    "# train <- function(x, y, hidden = 5, learn_rate = 1e-2, iterations = 1e4) {\n",
    "#   d <- ncol(x) + 1\n",
    "#   w1 <- matrix(rnorm(d * hidden), d, hidden)\n",
    "#   w2 <- as.matrix(rnorm(hidden + 1))\n",
    "#   for (i in 1:iterations) {\n",
    "#     ff <- feedforward(x, w1, w2)\n",
    "#     bp <- backpropagate(x, y,\n",
    "#                         y_hat = ff$output,\n",
    "#                         w1, w2,\n",
    "#                         h = ff$h,\n",
    "#                         learn_rate = learn_rate)\n",
    "#     w1 <- bp$w1; w2 <- bp$w2\n",
    "#   }\n",
    "#   list(output = ff$output, w1 = w1, w2 = w2)\n",
    "# }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using a framework (Flux.jl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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